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Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

Author

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  • İmdat İşcan

Abstract

A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

Suggested Citation

  • İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    • Handle: RePEc:hin:jjmath:346305
    DOI: 10.1155/2014/346305
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    Cited by:

    1. Praveen Agarwal & Mahir Kadakal & İmdat İşcan & Yu-Ming Chu, 2020. "Better Approaches for n -Times Differentiable Convex Functions," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    2. Saima Rashid & Aasma Khalid & Omar Bazighifan & Georgia Irina Oros, 2021. "New Modifications of Integral Inequalities via ℘ -Convexity Pertaining to Fractional Calculus and Their Applications," Mathematics, MDPI, vol. 9(15), pages 1-23, July.
    3. Shin Min Kang & Ghulam Abbas & Ghulam Farid & Waqas Nazeer, 2018. "A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results," Mathematics, MDPI, vol. 6(7), pages 1-16, July.
    4. Hüseyin Budak & Fatih Hezenci & Hasan Kara & Mehmet Zeki Sarikaya, 2023. "Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    5. Xia Wu & JinRong Wang & Jialu Zhang, 2019. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    6. Waqar Afzal & Alina Alb Lupaş & Khurram Shabbir, 2022. "Hermite–Hadamard and Jensen-Type Inequalities for Harmonical ( h 1 , h 2 )-Godunova–Levin Interval-Valued Functions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    7. Muhammad Aamir Ali & Fongchan Wannalookkhee & Hüseyin Budak & Sina Etemad & Shahram Rezapour, 2022. "New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
    8. Imran Abbas Baloch & İmdat İşcan, 2015. "Some Ostrowski Type Inequalities for Harmonically -Convex Functions in Second Sense," International Journal of Analysis, Hindawi, vol. 2015, pages 1-9, October.
    9. Muhammad Tariq & Soubhagya Kumar Sahoo & Sotiris K. Ntouyas & Omar Mutab Alsalami & Asif Ali Shaikh & Kamsing Nonlaopon, 2022. "Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    10. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    11. Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    12. Dafang Zhao & Ghazala Gulshan & Muhammad Aamir Ali & Kamsing Nonlaopon, 2022. "Some New Midpoint and Trapezoidal-Type Inequalities for General Convex Functions in q -Calculus," Mathematics, MDPI, vol. 10(3), pages 1-14, January.
    13. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    14. Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    15. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.

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